This is clearly a relaxation as for any GPT, we have \(K_A\subseteq {K^A}^*\) .
However, certain GPTs satisfy a property known as the No-Restriction Hypothesis [1]}, which states that \(K_A = {K^A}^*\) .
For such theories we have \(\widetilde{\mathcal {P}}_A=\mathcal {P}_A\)  and so the relaxation is trivial.
In particular this is the case for quantum theory.
Therefore, the proof of our main result greatly simplifies in the case of quantum theory and any other theory satisfying the No-Restriction Hypothesis.
